Hisob(Calculas)” fanidan talabalarning mustaqil ishlari uchun tavsiya etiladigan mavzular ro’yxati

Sonli qatorlar (musbat hadli qatorlarning yaqinlashish teoremalari, Leybnis teoremasi. Absolyut va shartli yaqinlashish).
Darajali qatorlar, yaqinlashish radiusi va yaqinlashish sohasi. Teylor formulasi va Teylor qatori.

3. Qatorning yaqinlashishini tekshiring:

4. Qatorning yaqinlashishini tekshiring:

5. Ishoralari almashinuvсhi qatorning shartli va absolyut yaqinlashishini tekshiring:

6. Qatorning yaqinlashish sohasini toping:

Ikki argumentli funksiyani aniqlanish sohasi, grafigi, limiti va uzluksizligi.

Birinchi va ikkinchi tartibli xususiy hosilalar. To‘la differensial, taqribiy hisoblash. Ikkinchi tartibli hosila va differensial.
Quydagi funksiyalarning x-bo‘yicha va y- bo‘yicha xususiy hosilalari va to‘la differensiali to’ilsin.
1. z= 2. z=

3. 4.

5. 6.

7. 8.

9. z=cosy+(y-x)siny; 10. z=x^yln

11. z=4tg(x -y ) 12. z=2cos (y-

13. ; 14. ;

15. 16. ;

17. 18.

19. z= 20. z=x

21. z= 22. z=xsin

23. z=xln ; 24. z=x ;

25. z=x ; 26. z=

27. z=xarctg 28. z=xcos

29. z=xctg ; 30. z=

Ikki o‘zgaruvchili funksiyaning ikkinchi tartibli xususiy hosilalari

Quydagi z=f(x:y) funksiya uchun ayniyatni isbotlang

1. z=

2. z=

3. z=ln(x²+y²+2x+1)

4. z=ln(x+e^-y)

5. z= x

6. z=xy;

7. z=x

8. z=sin(x+y)

9. z=cosy+(y-x)siny; (x-y)

10. z=x ln x

11. z=4y(x -y )

12. z=2cos (y- 2

13. z=xy+3y;

14. z=8y-x²-y²; x

15. z=3x(x+y)+4y(x+y)

16. z=xy+7y; x

17. z=2x

18. z=ln(x²+y²);

19. z= x

20. z=x x

21. z=

22. z=xsin x

23. z=xln ; x

24. z=x ; x

25. z=x ; x

26. z=

27. z=xarctg x

28. z=xcos x

29. z=xctg ; x

30. z=

Ikki karrali integral (ta’rifi va misollar, ikki karrali integral, integrallash tartibini o‘zgartirish).

Dekart va qutb koordinatalari sistemasida ikki karrali integrallar.

Ikki karrali integralning tatbiqlari. Ikki karrali integral yordamida yuza va jism hajmini hisoblash. Massa, o‘rta qiymat va inersiya momenti.

I va II – tur egri chiziqli integrallar (geometrik va fizik ma’nolari).Grin formulasi.

1.Integrallash tartibini o’zgartiring:

1.1 1.2

1.3 1.4

1.5 1.6

1.7 1.8

1.9 1.10

1.11 1.12

1.13 1.14

1.15 1.16

1.17 1.18

1.19 1.20

1.21 1.22

1.23 1.24

1.25 1.26

1.27 1.28

1.29 1.30

2.Berilgan chiziqlar bilan chegaralangan shaklning yuzini hisoblang:

2.1 2.2

2.3 2.4

2.5 2.6

2.7 2.8

2.9 2.10

2.11 2.12

2.13 2.14

2.15 2.16

2.17 2.18

2.19 2.20

2.21 2.22

2.23 2.24

2.25 2.26

2.27 2.28

2.29 2.30

3.Sirt zichligi ma’lum bo’sa, berilgan egri chiziqlar bilan chegaralangan plastinkaning massasini toping:

3.1 3.2

3.3 3.4

3.5 3.6

3.7 3.8

3.9 3.10

3.11 3.12

3.13 3.14

3.15 3.18

3.19 3.20

3.21 3.22

3.23 3.24

3.25 3.26

3.27 3.28

3.29 3.30

4.Egri chiziqli integralni xisoblang:

4.1

4.2

4.3

4.4

4.5

4.6

4.7

4.8

4.9

4.10

4.11

4.12

4.13

4.14

4.15

4.16

4.17

4.18

4.19

4.20

4.21

4.22

4.23

4.24

4.25

4.26

4.27

4.28

4.29

4.30

5. Egri chiziqli integralni xisoblang:

5.1

5.2

5.3

5.4

5.5

5.6

5.7

5.8

5.9

5.10

5.11

5.12

5.13

5.14

5.15

5.16

5.17

5.18

5.19

5.20

5.21

5.22

5.23

5.24

5.25

5.26

5.27

5.28

5.29

5.30

6. Berilgan ifodalar funksiyaning to’liq differesiali ekanligini ko’rsating. Rgri chiziqli integral yordamida funksiyani toping.

6.1

6.2

6.3

6.4

6.5

6.6

6.7

6.8

6.9

6.10

6.11

6.12

6.13

6.14

6.15

6.16

6.17

6.18

6.19

6.20

6.21

6.22

6.23

6.24

6.25

6.26

6.27

6.28

6.29

6.30